The £90m scheme will now be referred to the secretary of state for communities and local government for a final decision on the planning application.
This will allow the council to take the next steps of land acquisition and the appointment of a contractor for the scheme.
With £45m coming from central government and a target of £23m from developers set to benefit, the council is left to meet the funding gap of £22m.
The route of the planned road runs to the north of the town, south of Eaton. It will link the A534 Sandbach Road, near its junction with Sandy Lane, to the A536 Macclesfield Road, near its junction with Moss Lane and provide a new village crossing at the river Dane. It will create the potential for improved road connections to both Congleton Business Park and Radnor Park Trading Estate.
It is also expected to reduce traffic in the middle of Congleton.
Councillor David Brown, Cheshire East Council cabinet member for highways & infrastructure, said: "I am pleased that both Cabinet and the strategic planning board have reached these decisions. This is the biggest road infrastructure scheme undertaken by this council and I know it will be of enormous relief to many people in Congleton to know that it is proceeding.
"The link road will relieve traffic congestion in Congleton and, as a result, will boost the local economy by opening up new sites for development and create new opportunities for businesses and workers."